Q.LOG is v3's q48_log_approx: x = 2^k * m with 1.0 <= m < 2.0, ln m by
up to 6 Newton rounds on e^y = m, result y + k * ln 2. As ruled, e^y is
Q.EXP's Taylor loop written in line rather than a call to Q.EXP, so
Q.LOG calls only Q.*, Q./ and UM*. After the reduction m, y, the Taylor
term and its sum each fit one cell, so the 7-cell variable (QL) holds
single cells. x <= 0 returns 0 and sets NODE-ERROR (D-12).
Checked bit for bit against v3's q48_log_approx (ported into the test)
on 22 positive edge values, 2000 pseudo-random x of every magnitude and
a sweep of every 17th reduced m, at 32- and 64-bit cells, optimised and
ASan+UBSan (`make test`, `make sanitize`). Mutating the round count, the
100-ulp stop, ln 2 or the Taylor length all fail.
v3's clamp y = max(y - corr, 0) is kept but cannot fire: a scan of all
65536 values of m in C never reaches it, and never needs more than 4
rounds. So no test covers it.
The test harness's per-call step limit is raised from 100000 to 4000000
instruction words: a 64-bit Q./ takes about 6500, and a mutant forcing
extra Newton rounds ran past the old limit and looked like a width
difference.
Headroom (data under arg / return): Q.LOG 3/2.
Test results on the amd64 host only. This is a development check, not
acceptance (JUSTIFICATION.md section 16).
Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
